The graph of a function is the set of ordered pairs (x, y) for which f of x equals y. When both the input and the output are real numbers, these pairs become points in the Cartesian plane that usually trace out a curve when plotted, a picture commonly called a plot. For a function of two variables, the graph instead consists of ordered triples (x, y, z) with f of x and y equal to z, forming a surface in three dimensions rather than a curve. The graph is a basic tool for visualizing a function across mathematics, science, engineering, finance and technology, and while modern set theory sometimes treats a function as identical to its graph, it remains useful to keep the two ideas separate, since the graph alone fixes a function's domain and range but not its codomain.
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Source Graph of a Function (Wikipedia)
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1. Graph of a Function (Wikipedia)
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In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs ( x, y) {\displaystyle (x,y)}, where f ( x) = y. {\displaystyle f(x)=y.} In the common case where x {\displaystyle x} and f ( x) {\displaystyle f(x)} are real numbers, these pairs are Cartesian coordinates of points in a plane and often form a curve.
In Branch: Set Theory, Lead paragraph
In the modern foundations of mathematics, and, typically, in set theory, a function is actually equal to its graph.
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